Groupoid Actions on Fractafolds

We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault–Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault–Deaconu groupoid itself. We also show that when the bundle is locally compact the associated $C^*$-algebra is primitive and has a densely defined lower-semicontinuous trace.